Question: Rewrite as a simplified fraction. ${0.60\overline{1} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 601.1111...\\ 100x &= 60.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 541}$ ${x = \dfrac{541}{900}} $